IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v7y2019i1p7-d196509.html
   My bibliography  Save this article

Surplus Sharing with Coherent Utility Functions

Author

Listed:
  • Delia Coculescu

    (Institut für Banking und Finance, Universität Zürich, Plattenstrasse 32, 8032 Zürich, Switzerland)

  • Freddy Delbaen

    (Departement für Mathematik, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
    Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland)

Abstract

We use the theory of coherent measures to look at the problem of surplus sharing in an insurance business. The surplus share of an insured is calculated by the surplus premium in the contract. The theory of coherent risk measures and the resulting capital allocation gives a way to divide the surplus between the insured and the capital providers, i.e., the shareholders.

Suggested Citation

  • Delia Coculescu & Freddy Delbaen, 2019. "Surplus Sharing with Coherent Utility Functions," Risks, MDPI, vol. 7(1), pages 1-12, January.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:1:p:7-:d:196509
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/7/1/7/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/7/1/7/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    2. Deprez, Olivier & Gerber, Hans U., 1985. "On convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 4(3), pages 179-189, July.
    3. DELBAEN, Freddy, 1974. "Convex games and extreme points," LIDAM Reprints CORE 159, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bielecki Tomasz R. & Cialenco Igor & Pitera Marcin & Schmidt Thorsten, 2020. "Fair estimation of capital risk allocation," Statistics & Risk Modeling, De Gruyter, vol. 37(1-2), pages 1-24, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Delia Coculescu & Freddy Delbaen, 2022. "Fairness principles for insurance contracts in the presence of default risk," Mathematical Finance, Wiley Blackwell, vol. 32(2), pages 595-626, April.
    2. Aouani, Zaier & Chateauneuf, Alain, 2008. "Exact capacities and star-shaped distorted probabilities," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 185-194, September.
    3. Qiqi Li & Wei Wang & Yiying Zhang, 2024. "Self-protection and insurance demand with convex premium principles," Papers 2411.19436, arXiv.org.
    4. Young, Virginia R., 1999. "Optimal insurance under Wang's premium principle," Insurance: Mathematics and Economics, Elsevier, vol. 25(2), pages 109-122, November.
    5. Stanislaw Heilpern, 2002. "Using Choquet integral in economics," Statistical Papers, Springer, vol. 43(1), pages 53-73, January.
    6. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A., 2010. "Decision principles derived from risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 294-302, December.
    7. Sung, K.C.J. & Yam, S.C.P. & Yung, S.P. & Zhou, J.H., 2011. "Behavioral optimal insurance," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 418-428.
    8. Wang, Ruodu & Zitikis, Ričardas, 2020. "Weak comonotonicity," European Journal of Operational Research, Elsevier, vol. 282(1), pages 386-397.
    9. Carlier, G. & Dana, R. A., 2003. "Core of convex distortions of a probability," Journal of Economic Theory, Elsevier, vol. 113(2), pages 199-222, December.
    10. Zuo Quan Xu, 2021. "Moral-hazard-free insurance: mean-variance premium principle and rank-dependent utility theory," Papers 2108.06940, arXiv.org, revised Aug 2022.
    11. Gao, Feng & Song, Fengming & Zhang, Lihong, 2007. "Coherent risk measure, equilibrium and equilibrium pricing," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 85-94, January.
    12. Carlier, G., 2005. "Representation of the core of convex measure games via Kantorovich potentials," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 898-912, November.
    13. Król, Michał, 2012. "Product differentiation decisions under ambiguous consumer demand and pessimistic expectations," International Journal of Industrial Organization, Elsevier, vol. 30(6), pages 593-604.
    14. Filiz-Ozbay, Emel & Guryan, Jonathan & Hyndman, Kyle & Kearney, Melissa & Ozbay, Erkut Y., 2015. "Do lottery payments induce savings behavior? Evidence from the lab," Journal of Public Economics, Elsevier, vol. 126(C), pages 1-24.
    15. ,, 2014. "Second order beliefs models of choice under imprecise risk: non-additive second order beliefs vs. nonlinear second order utility," Theoretical Economics, Econometric Society, vol. 9(3), September.
    16. Stephen P. Jenkins & Philippe Van Kerm, 2016. "Assessing Individual Income Growth," Economica, London School of Economics and Political Science, vol. 83(332), pages 679-703, October.
    17. Goovaerts, M. J. & Dhaene, J., 1999. "Supermodular ordering and stochastic annuities," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 281-290, May.
    18. Haliassos, Michael & Hassapis, Christis, 2001. "Non-expected Utility, Saving and Portfolios," Economic Journal, Royal Economic Society, vol. 111(468), pages 69-102, January.
    19. Mohammed Abdellaoui & Olivier L’Haridon & Horst Zank, 2010. "Separating curvature and elevation: A parametric probability weighting function," Journal of Risk and Uncertainty, Springer, vol. 41(1), pages 39-65, August.
    20. Charles Condevaux & Stéphane Mussard & Téa Ouraga & Guillaume Zambrano, 2020. "Generalized Gini linear and quadratic discriminant analyses," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 219-236, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jrisks:v:7:y:2019:i:1:p:7-:d:196509. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.